Advertisement

Quark and gluon contributions to the QCD trace anomaly

  • Yoshitaka HattaEmail author
  • Abha Rajan
  • Kazuhiro Tanaka
Open Access
Regular Article - Theoretical Physics

Abstract

We show that, in dimensional regularization in the minimal subtraction scheme, the QCD trace anomaly can be unambiguously decomposed into two parts coming from the renormalized quark and gluon energy momentum tensors. We carry out this decomposition at the two-loop level. The result can be used to constrain the renormalization group properties of the nucleon’s twist-four gravitational form factor \( {\overline{C}}_{q,g} \).

Keywords

Anomalies in Field and String Theories Renormalization Group 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    X.-D. Ji, Gauge-invariant decomposition of nucleon spin, Phys. Rev. Lett. 78 (1997) 610 [hep-ph/9603249] [INSPIRE].
  2. [2]
    S. Kumano, Q.-T. Song and O.V. Teryaev, Hadron tomography by generalized distribution amplitudes in pion-pair production process γ γπ 0 π 0 and gravitational form factors for pion, Phys. Rev. D 97 (2018) 014020 [arXiv:1711.08088] [INSPIRE].
  3. [3]
    M.V. Polyakov and P. Schweitzer, Forces inside hadrons: pressure, surface tension, mechanical radius and all that, Int. J. Mod. Phys. A 33 (2018) 1830025 [arXiv:1805.06596] [INSPIRE].
  4. [4]
    K. Tanaka, Operator relations for gravitational form factors of a spin-0 hadron, Phys. Rev. D 98 (2018) 034009 [arXiv:1806.10591] [INSPIRE].
  5. [5]
    National Academies of Sciences, Engineering and Medicine, An assessment of U.S.-based electron-ion collider science, National Academies Press, Washington, DC, U.S.A., (2018).Google Scholar
  6. [6]
    S. Joosten and Z.E. Meziani, Heavy quarkonium production at threshold: from JLab to EIC, PoS(QCDEV2017)017, (2018) [arXiv:1802.02616] [INSPIRE].
  7. [7]
    D. Kharzeev, H. Satz, A. Syamtomov and G. Zinovjev, J/ψ photoproduction and the gluon structure of the nucleon, Eur. Phys. J. C 9 (1999) 459 [hep-ph/9901375] [INSPIRE].
  8. [8]
    Y. Hatta and D.-L. Yang, Holographic J/ψ production near threshold and the proton mass problem, Phys. Rev. D 98 (2018) 074003 [arXiv:1808.02163] [INSPIRE].
  9. [9]
    N.K. Nielsen, The energy momentum tensor in a non-Abelian quark gluon theory, Nucl. Phys. B 120 (1977) 212 [INSPIRE].
  10. [10]
    R. Tarrach, The renormalization of FF, Nucl. Phys. B 196 (1982) 45 [INSPIRE].
  11. [11]
    J.C. Collins, Renormalization: an introduction to renormalization, the renormalization group, and the operator product expansion, Cambridge University Press, Cambridge, U.K., (1984).Google Scholar
  12. [12]
    H. Suzuki, Energy-momentum tensor from the Yang-Mills gradient flow, PTEP 2013 (2013) 083B03 [Erratum ibid. 2015 (2015) 079201] [arXiv:1304.0533] [INSPIRE].
  13. [13]
    X.-D. Ji, W. Melnitchouk and X. Song, A study of off forward parton distributions, Phys. Rev. D 56 (1997) 5511 [hep-ph/9702379] [INSPIRE].
  14. [14]
    V.M. Braun and A. Lenz, On the SU(3) symmetry-breaking corrections to meson distribution amplitudes, Phys. Rev. D 70 (2004) 074020 [hep-ph/0407282] [INSPIRE].
  15. [15]
    E.V. Shuryak and A.I. Vainshtein, Theory of power corrections to deep inelastic scattering in quantum chromodynamics. 1. Q 2 effects, Nucl. Phys. B 199 (1982) 451 [INSPIRE].
  16. [16]
    A.P. Bukhvostov, E.A. Kuraev and L.N. Lipatov, Deep inelastic electron scattering by a polarized target in quantum chromodynamics, JETP Lett. 37 (1983) 482 [Pisma Zh. Eksp. Teor. Fiz. 37 (1983) 406] [Sov. Phys. JETP 60 (1984) 22] [Zh. Eksp. Teor. Fiz. 87 (1984) 37] [INSPIRE].
  17. [17]
    I.I. Balitsky and V.M. Braun, Evolution equations for QCD string operators, Nucl. Phys. B 311 (1989) 541 [INSPIRE].
  18. [18]
    J. Kodaira, Y. Yasui, K. Tanaka and T. Uematsu, QCD corrections to the nucleon’s spin structure function g 2(x, Q 2), Phys. Lett. B 387 (1996) 855 [hep-ph/9603377] [INSPIRE].
  19. [19]
    J. Kodaira, T. Nasuno, H. Tochimura, K. Tanaka and Y. Yasui, Renormalization of gauge invariant operators for the structure function g 2(x, Q 2), Prog. Theor. Phys. 99 (1998) 315 [hep-ph/9712395] [INSPIRE].
  20. [20]
    J. Kodaira and K. Tanaka, Polarized structure functions in QCD, Prog. Theor. Phys. 101 (1999) 191 [hep-ph/9812449] [INSPIRE].
  21. [21]
    T. Nishikawa and K. Tanaka, QCD sum rules for quark-gluon three-body components in the B meson, Nucl. Phys. B 879 (2014) 110 [arXiv:1109.6786] [INSPIRE].
  22. [22]
    M.V. Polyakov and H.-D. Son, Nucleon gravitational form factors from instantons: forces between quark and gluon subsystems, JHEP 09 (2018) 156 [arXiv:1808.00155] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    E.G. Floratos, C. Kounnas and R. Lacaze, Higher order QCD effects in inclusive annihilation and deep inelastic scattering, Nucl. Phys. B 192 (1981) 417 [INSPIRE].
  24. [24]
    S.A. Larin, P. Nogueira, T. van Ritbergen and J.A.M. Vermaseren, The three loop QCD calculation of the moments of deep inelastic structure functions, Nucl. Phys. B 492 (1997) 338 [hep-ph/9605317] [INSPIRE].
  25. [25]
    H. Makino and H. Suzuki, Lattice energy-momentum tensor from the Yang-Mills gradient flow — inclusion of fermion fields, PTEP 2014 (2014) 063B02 [Erratum ibid. 2015 (2015) 079202] [arXiv:1403.4772] [INSPIRE].
  26. [26]
    Y. Hatta, K. Tanaka and S. Yoshida, Twist-three relations of gluonic correlators for the transversely polarized nucleon, JHEP 02 (2013) 003 [arXiv:1211.2918] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    E. Leader, A critical assessment of the angular momentum sum rules, Phys. Lett. B 720 (2013) 120 [Erratum ibid. B 726 (2013) 927] [arXiv:1211.3957] [INSPIRE].
  28. [28]
    D. Chakrabarti, C. Mondal and A. Mukherjee, Gravitational form factors and transverse spin sum rule in a light front quark-diquark model in AdS/QCD, Phys. Rev. D 91 (2015) 114026 [arXiv:1505.02013] [INSPIRE].
  29. [29]
    X. Ji, X. Xiong and F. Yuan, Transverse polarization of the nucleon in parton picture, Phys. Lett. B 717 (2012) 214 [arXiv:1209.3246] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Yoshitaka Hatta
    • 1
    • 2
    Email author
  • Abha Rajan
    • 1
  • Kazuhiro Tanaka
    • 3
    • 4
  1. 1.Physics Department, Brookhaven National LaboratoryUptonU.S.A.
  2. 2.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  3. 3.Department of PhysicsJuntendo UniversityInzaiJapan
  4. 4.J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEKTokaiJapan

Personalised recommendations